ABSTRACT In deconvolution in with mixing density and kernel h, the mixture density is estimated with MDE having upper -error rate, in probability or in risk; . In one application, consists of -separable densities in R with differences changing sign at most J times and Totally Positive. When h is known and p is -smooth, vanishing outside a compact in plug-in upper bounds are provided for the -error rate of and its -th mixed partial derivative via , with rates and , respectively, for h super-smooth and smooth; . For the former rate is optimal for any and the latter misses the optimal by the factor when . and appear in optimal rates and lower error and risk bounds in the deconvolution literature.

中文翻译：

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去卷积中的插件 L2 误差上限，用于 Rd 中的混合密度估计及其导数，通过混合物的 L1 误差

摘要 在混合密度和核 h 的反卷积中，混合密度用具有较高错误率、概率或风险的 MDE 估计；. 在一个应用程序中，由 R 中的可分离密度组成，差异最多改变符号 J 次且完全为正。当 h 已知且 p 为 -smooth 时，为 h 的 -error rate 及其第 -th 混合偏导数提供了消失在插件上限的紧凑外，分别具有 rate 和 ，对于 h 超平滑和平滑; . 因为前者的速率对于任何一个都是最优的，而后者在 时因因子而错过了最优值。并且在解卷积文献中以最优速率和较低的错误和风险界限出现。